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NPS calculator: Net Promoter Score with its margin of error
Convertica's free NPS® calculator works out a Net Promoter Score℠ from promoter, passive and detractor counts, from the number of responses at each score, or from a pasted column of scores. It also gives the margin of error for your sample size, and tests whether a change since your last survey is larger than the noise.
Short answer
An NPS calculator turns survey answers into a Net Promoter Score: the percentage of promoters (scores of 9 or 10) minus the percentage of detractors (0 to 6), from -100 to 100. Convertica's free NPS calculator takes group counts, a count per score or a pasted column of scores, and adds the margin of error.
- NPS = % promoters - % detractors. Passives (7 or 8) count in the total but are neither added nor subtracted.
- The result is a whole number from -100 to 100, not a percentage.
- Every NPS has a margin of error. The example of 400 responses is 30 ± 7.7 points at 95% confidence.
- An NPS can need up to four times the responses a single percentage needs for the same margin of error.
- A change between two surveys only means something when it is larger than the noise in both of them.
Calculate your Net Promoter Score
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Net Promoter Score
30
- Detractors (0 to 6) 80 20.0%
- Passives (7 to 8) 120 30.0%
- Promoters (9 to 10) 200 50.0%
400 responses: 50.0% promoters minus 20.0% detractors = 30.0.
Margin of error: ±7.7 points at 95% confidence, which is 22.3 to 37.7. This is the simple formula.
Adjusted 95% confidence interval: 22.2 to 37.4. At this sample size the two nearly agree.
Read it as: ranges built this way contain the score of your whole customer base in about 95% of surveys. That covers sampling error only, not who chose to answer.
Formula
NPS = (promoters - detractors) / responses * 100
margin of error = z * sqrt((p + d - (p - d)^2) / n) * 100
p = promoters / n, d = detractors / n, z = 1.96 at 95% confidenceCompare two NPS surveys
This quarter against last quarter, or one segment against another. Tests whether the gap is larger than sampling noise.
Change in NPS
+8.0 points
Current 30.0 from 400 responses, previous 22.0 from 400.
Not larger than the noise at 95% confidence: the interval for the change, -3.0 to +18.9 points, includes 0.
Margin of error of the change: ±11.0 points. With samples of this size, a move smaller than that cannot be told apart from sampling noise.
z = 1.42, two-sided p-value 0.1557 (adjusted Wald test).
This assumes two separate random samples. If the same people answered both surveys, it does not apply.
Formula
adjust each survey : promoters + 3/4, detractors + 3/4, responses + 3
v = p + d - (p - d)^2 from the adjusted shares
standard error = sqrt(v1 / n1 + v2 / n2)
interval = (NPS1 - NPS2) ± z * standard errorHow to use the NPS calculator
Pick the way in that matches the data you have. All three give the same score for the same survey, because each one ends in the same three numbers: promoters, passives and detractors.
| You have | Choose | Enter |
|---|---|---|
| A dashboard that already shows the three groups | Group counts | The number of promoters, passives and detractors |
| A chart or table of how many people gave each score | A count per score | The number of responses at each score from 0 to 10 |
| A spreadsheet export with one row per response | A list of scores | The score column, pasted as it is |
- Enter the survey. Use every completed answer to the recommend question, including the 7s and 8s.
- Read the score and the bar under it, which shows the share of each group.
- Read the margin of error. It tells you how far the score could move if you ran the same survey again on a different sample of the same customers.
- Comparing with an earlier survey? Put both sets of counts into the second calculator before you call the change a rise or a fall.
What is a Net Promoter Score?
A Net Promoter Score (NPS) is a single number from -100 to 100 that sums up how customers answer one question: how likely they are to recommend a company to a friend or colleague, on a scale from 0 to 10. It is the percentage who answer 9 or 10 minus the percentage who answer 0 to 6.
The question and the grouping come from Frederick F. Reichheld's article The One Number You Need to Grow, published in Harvard Business Review in December 2003. It asked customers "How likely is it that you would recommend our company to a friend or colleague?" and sorted the answers into three groups.
| Group | Score given | In the formula |
|---|---|---|
| Promoters | 9 or 10 | Added |
| Passives | 7 or 8 | Counted in the total only |
| Detractors | 0 to 6 | Subtracted |
Two details trip people up. The scale has eleven points, not ten, because it starts at 0. And the result is not a percentage: it is the gap between two percentages, written as a whole number. Bain & Company, whose team developed the measure with Reichheld, describes the same scoring on its page about measuring your Net Promoter Score.
What is the NPS formula?
The NPS formula is the number of promoters minus the number of detractors, divided by the total number of responses, times 100. Passives are part of the total but are not added or subtracted. The answer runs from -100, when everyone is a detractor, to 100, when everyone is a promoter.
NPS = (promoters - detractors) / (promoters + passives + detractors) * 100
= % promoters - % detractorsWorked example: from the three counts
A survey gets 400 responses: 200 promoters, 120 passives and 80 detractors. These are the default values in the calculator, made up to show the arithmetic. They are not a benchmark.
- Promoters: 200 / 400 = 50%.
- Detractors: 80 / 400 = 20%.
- NPS: 50% - 20% = 30.
The 120 passives (30%) appear nowhere in step 3, but they are in the 400 that steps 1 and 2 divide by. Drop them from the total and the same survey would seem to score far higher than 30.
Worked example: from a count for each score
The same survey, as a survey tool would chart it. Add up the rows for each group, then use the formula.
| Score | Responses | Group |
|---|---|---|
| 0 | 4 | Detractor |
| 1 | 4 | Detractor |
| 2 | 6 | Detractor |
| 3 | 8 | Detractor |
| 4 | 12 | Detractor |
| 5 | 20 | Detractor |
| 6 | 26 | Detractor |
| 7 | 50 | Passive |
| 8 | 70 | Passive |
| 9 | 90 | Promoter |
| 10 | 110 | Promoter |
Scores 0 to 6 add up to 80 detractors, 7 and 8 to 120 passives, 9 and 10 to 200 promoters: the same three counts, and the same NPS of 30.
What is the margin of error of an NPS?
The margin of error of an NPS is how far the score could sit from the true figure for all your customers, through the luck of who answered. It depends on the number of responses and on how split they are. The example survey of 400 responses scores 30 with a margin of error of ±7.7 points at 95% confidence.
To get it, score every response +1 for a promoter, 0 for a passive and -1 for a detractor. The NPS is the average of those values, and their variance is the share of promoters plus the share of detractors, minus the squared gap between the two. This is the standard variance of a difference between two shares of the same sample, and Brendan Rocks sets it out for the NPS in Interval Estimation for the Net Promoter Score (The American Statistician, 2016).
variance = p + d - (p - d)^2
standard error = sqrt(variance / n)
margin of error = z * standard error * 100Worked example: the margin of error on 400 responses
- Shares: p = 0.50 promoters, d = 0.20 detractors, so p - d = 0.30.
- Variance: 0.50 + 0.20 - 0.30² = 0.50 + 0.20 - 0.09 = 0.61.
- Standard error: √(0.61 / 400) = √0.001525 = 0.0391.
- Margin of error at 95%: 1.96 × 0.0391 = 0.0765, or ±7.7 points.
- So the NPS is 30 ± 7.7: anywhere from 22.3 to 37.7.
A margin that wide surprises people, because a single survey percentage from 400 responses has a margin of at most ±4.9 points. An NPS is a difference between two shares, and both of them wobble. In the widest case, half promoters and half detractors, the margin of error of an NPS is exactly twice that of a single percentage, so it takes four times the responses to match its precision.
| Responses | Example shares (50% promoters, 20% detractors) | Widest NPS case (half promoters, half detractors) | A single percentage at 50%, for comparison |
|---|---|---|---|
| 50 | ±21.6 | ±27.7 | ±13.9 |
| 100 | ±15.3 | ±19.6 | ±9.8 |
| 200 | ±10.8 | ±13.9 | ±6.9 |
| 400 | ±7.7 | ±9.8 | ±4.9 |
| 1,000 | ±4.8 | ±6.2 | ±3.1 |
| 2,500 | ±3.1 | ±3.9 | ±2.0 |
| 10,000 | ±1.5 | ±2.0 | ±1.0 |
Read across the 100 row: an NPS from 100 responses with these shares is good to about ±15.3 points. Two such surveys could land 15.3 points apart with nothing having changed. For the margin of error of an ordinary survey percentage, use the margin of error calculator, and for the interval around a mean or a conversion rate, the confidence interval calculator.
Why the calculator also shows an adjusted interval
The simple formula is a normal approximation, and with few responses it is too confident. In the paper cited above, Rocks tested a range of interval methods on simulated samples and on real survey data and found that the plain version covered the true score less often than its stated level. The closed-form method that did best adds three quarters of a response to the promoters, three quarters to the detractors and one and a half to the passives before using the same formula. That is the adjusted interval in the result panel.
The table shows how often each "95%" interval really contains the true score. Nothing in it is simulated: for each row, every possible survey of that size is listed, and the probabilities of the ones whose interval contains the true score are added up.
| True shares | True NPS | Responses | Simple interval | Adjusted interval |
|---|---|---|---|---|
| 50% promoters, 30% passives, 20% detractors | 30 | 10 | 89.6% | 96.2% |
| 50% promoters, 30% passives, 20% detractors | 30 | 20 | 92.6% | 94.8% |
| 50% promoters, 30% passives, 20% detractors | 30 | 50 | 94.1% | 95.0% |
| 50% promoters, 30% passives, 20% detractors | 30 | 100 | 94.5% | 94.9% |
| 50% promoters, 30% passives, 20% detractors | 30 | 200 | 94.7% | 95.0% |
| 80% promoters, 15% passives, 5% detractors | 75 | 10 | 88.4% | 94.4% |
| 80% promoters, 15% passives, 5% detractors | 75 | 20 | 86.0% | 95.6% |
| 80% promoters, 15% passives, 5% detractors | 75 | 50 | 93.1% | 95.6% |
| 80% promoters, 15% passives, 5% detractors | 75 | 100 | 93.5% | 95.4% |
| 80% promoters, 15% passives, 5% detractors | 75 | 200 | 94.4% | 95.2% |
With 10 responses the simple interval is right 89.6% of the time, not 95%. When nearly everyone is a promoter it is worse: 86.0% at 20 responses. The adjusted interval stays close to 95% throughout, and by 200 responses the two barely differ (94.7% against 95.0%).
Either interval covers sampling error only. It assumes the people who answered are a random sample of the customers you care about. It cannot correct for who chose to reply, for when you asked, or for a survey sent only to recent buyers. Those gaps can be larger than the margin of error, and no formula on this page measures them.
Is a change in NPS real, or noise?
A change in NPS is more than noise when the confidence interval for the difference between the two surveys does not include 0. That interval is wider than either survey's own margin of error, because both scores carry sampling noise. In the example, a rise from 22 to 30 on 400 responses each is not larger than the noise.
Worked example: 22 last quarter, 30 this quarter
Both surveys have 400 responses. These are the default values in the second calculator, made up to show the arithmetic.
- Adjust each survey: add ¾ to the promoters, ¾ to the detractors and 3 to the responses, which makes 403 in each. The adjusted scores are 0.2978 and 0.2184, a difference of 0.0794.
- Variance of each, from the adjusted shares: 0.6098 and 0.6508.
- Standard error of the difference: √(0.6098 / 403 + 0.6508 / 403) = 0.0559.
- Margin of error of the change at 95%: 1.96 × 0.0559 = ±11.0 points.
- Interval for the change: -3.0 to +18.9 points. It includes 0, so the 8 point rise could be sampling noise (z = 1.42, p = 0.1557).
The method is the adjusted interval from the section above, applied to both surveys, as described by Jim Lewis and Jeff Sauro in How to Statistically Compare Two Net Promoter Scores. The table keeps the same shares and the same 8 point gap, and only raises the number of responses.
| Responses in each survey | Margin of error of the change | Interval for the change (points) | p-value | Verdict |
|---|---|---|---|---|
| 400 | ±11.0 | -3.0 to +18.9 | 0.1557 | Inside the noise |
| 800 | ±7.8 | +0.2 to +15.7 | 0.0443 | Larger than the noise |
| 1,600 | ±5.5 | +2.5 to +13.5 | 0.0044 | Larger than the noise |
| 4,000 | ±3.5 | +4.5 to +11.5 | below 0.0001 | Larger than the noise |
The same move clears the noise at 800 responses in each survey. So before a change in NPS goes into a report, check three things:
- Is it larger than the noise? Run both sets of counts through the comparison. Do not compare two separate margins of error by eye.
- Were the two surveys run the same way? The same question wording, the same channel, the same point in the customer's journey. A score from an email sent a week after delivery and a score from a pop-up on the order confirmation page are not the same measurement.
- Are they separate samples? The test assumes two independent groups of respondents. If the same people answered both times, it does not apply.
An A/B test asks the same question about two conversion rates, and answers it the same way, with an interval for the difference. For that, use the statistical significance calculator, and see the A/B testing guide for how to read a result once you have one.
How many responses do you need for an NPS survey?
The number of responses an NPS survey needs depends on the margin of error you can live with. In the widest case, a margin of ±10 points at 95% confidence takes 385 responses and ±5 points takes 1,537. Halving the margin of error takes four times as many.
responses needed = z^2 * variance / (margin of error / 100)^2 rounded up
variance is at most 1: use 1 when you have no earlier survey to go on| Margin of error | Widest case (half promoters, half detractors) | Example shares (50% promoters, 20% detractors) |
|---|---|---|
| ±10 points | 385 | 235 |
| ±5 points | 1,537 | 938 |
| ±3 points | 4,269 | 2,604 |
| ±2 points | 9,604 | 5,859 |
| ±1 point | 38,415 | 23,433 |
These are completed responses, not invitations sent. If you already have a survey, put its variance into the formula instead of the widest case: the calculator's worked steps above show where it comes from. With fewer responses than the table asks for, the score is still worth reading. Report it with its margin of error, and read the comments.
The paste box in the calculator starts with a small survey of 20 answers to make the point: 12 promoters, 5 passives and 3 detractors score 45, with an adjusted 95% interval of 8.4 to 69.8. That range is too wide to rank it against anything.
What is a good NPS?
A good NPS is one that is higher than your own last reading by more than the margin of error, measured the same way. There is no universal pass mark, and this page does not print one. A score depends on who was asked, how and when, so a figure from another company is rarely a fair comparison.
- Above 0 means more promoters than detractors. That is the only threshold the arithmetic itself gives you.
- Your own trend is the comparison you control: the same question, sent the same way, to the same kind of customer.
- The margin of error tells you whether a step in that trend is a step at all.
- Segments can differ where the total hides it: new customers against repeat customers, or one product against another. Check each gap with the comparison calculator, because segments are smaller samples.
A published benchmark comes from someone else's sample and someone else's survey method. If you use one, compare like with like and ask how many responses are behind it.
How to calculate NPS in Excel or Google Sheets
To calculate NPS in Excel or Google Sheets, count the scores of 9 and 10, subtract the count of scores from 0 to 6, divide by the number of scores and multiply by 100. With one score per row in A2 to A401, these formulas work in both.
| You want | Formula |
|---|---|
| Promoters | =COUNTIF(A2:A401,">=9") |
| Detractors | =COUNTIF(A2:A401,"<=6") |
| Responses | =COUNT(A2:A401) |
| NPS | =100*(COUNTIF(A2:A401,">=9")-COUNTIF(A2:A401,"<=6"))/COUNT(A2:A401) |
| Margin of error at 95% | =100*NORM.S.INV(0.975)*SQRT(((D1+D2)/D3-((D1-D2)/D3)^2)/D3) |
Use COUNT for the total, not the number of rows: it skips blank cells and text, so unanswered rows do not dilute the score. For 90% confidence replace 0.975 with 0.95, and for 99% use 0.995. Or paste the column into the calculator above.
What does NPS have to do with conversion rate?
NPS and conversion rate sit on either side of the sale. Conversion rate counts what visitors do before they buy. NPS records what customers say afterwards. Neither one explains the other, but the comments that come with an NPS survey are useful raw material for improving the pages that convert.
- Promoters tell you what to say. The reasons people give for a 9 or 10 are the benefits in their own words. That is the customer language a headline or a product page needs. The conversion copywriting guide covers how to collect and use it.
- Detractors tell you what to fix or test. A complaint that repeats, such as a delivery date that was not clear at checkout, is a hypothesis for an A/B test.
- Both need the same statistics. A conversion rate from a slow week and an NPS from 50 responses are both small samples. Put an interval on each before acting on a change.
An NPS survey only reaches people who became customers. It says nothing about the visitors who left before buying. Convertica's free CRO audit looks at the page they left: eight checks, each scored out of 100, and three fixes to make first.
Related calculators
An NPS is one survey statistic among several. These tools cover the questions next to it.
See all free tools and how they fit together.
NPS calculator FAQ
What does an NPS calculator do?
An NPS calculator turns answers to the 0 to 10 likelihood-to-recommend question into a Net Promoter Score. It counts promoters (9 or 10), passives (7 or 8) and detractors (0 to 6), then subtracts the percentage of detractors from the percentage of promoters. This one also gives the margin of error and compares two surveys.
How do you calculate NPS?
Subtract the percentage of detractors from the percentage of promoters. With 200 promoters, 120 passives and 80 detractors out of 400 responses, that is 50% minus 20%, an NPS of 30. The percent sign is dropped: the score is reported as a whole number from -100 to 100.
Do passives count in NPS?
Yes, in the total. Passives, the people who answer 7 or 8, are part of the number of responses that both percentages are divided by, but they are neither added nor subtracted. Leaving them out of the total is a mistake that makes the score look more extreme than it is.
Is NPS a percentage?
No. NPS is the difference between two percentages, reported as a whole number without a percent sign. It runs from -100, when every response is a detractor, to 100, when every response is a promoter. A score of 0 means promoters and detractors are equal in number.
Can NPS be negative?
Yes. NPS is negative whenever detractors outnumber promoters. A survey with 20% promoters and 35% detractors has an NPS of -15. A negative score is a real result, not an error in the calculation.
What is a good NPS?
There is no universal number, and this page does not give one. A score depends on who was asked, when and how, so figures from other companies are rarely comparable with yours. The useful comparison is your own previous score, gathered the same way, and whether the change is larger than the margin of error.
What is the margin of error of an NPS?
The margin of error of an NPS is the range around the score that sampling alone can explain. For the 400 responses in the example it is ±7.7 points at 95% confidence, so an NPS of 30 could be anywhere from 22.3 to 37.7. It shrinks with the square root of the number of responses, and is widest when promoters and detractors are evenly split.
How many responses do I need for an NPS survey?
Up to 385 responses for a margin of error of ±10 points at 95% confidence, and up to 1,537 for ±5 points. Those are the widest case, half promoters and half detractors: a survey with passives in it needs fewer. Halving the margin of error takes four times the responses.
How do I know if a change in NPS is statistically significant?
Calculate one confidence interval for the difference between the two scores, using the promoters, passives and detractors of both surveys. If the interval does not include 0, the change is larger than sampling noise. In the example on this page, a rise from 22 to 30 on 400 responses each is not.
Can I calculate NPS from a 1 to 5 or 1 to 10 scale?
Not as a standard NPS. The published method uses an 11-point scale from 0 to 10, with 9 and 10 as promoters and 0 to 6 as detractors, and this calculator accepts only that scale. Any mapping from another scale is your own convention, so say which one you used when you report the score.
Is NPS the same as CSAT?
No. NPS comes from one question about how likely someone is to recommend you, and subtracts detractors from promoters. A customer satisfaction score (CSAT) usually asks how satisfied someone was with a purchase or an interaction and reports the share who chose a satisfied answer. This calculator works out NPS only.
Is this a National Pension System calculator?
No. This page calculates the Net Promoter Score from customer survey answers. It does not estimate a pension, a corpus or an annuity for India's National Pension System, which shares the abbreviation NPS.
Net Promoter®, NPS®, NPS Prism®, and the NPS-related emoticons are registered trademarks of Bain & Company, Inc., NICE Systems, Inc., and Fred Reichheld. Net Promoter Score℠ and Net Promoter System℠ are service marks of Bain & Company, Inc., NICE Systems, Inc., and Fred Reichheld.